FOURIER SERIES

The value of cos $2\pi$  and cos $\pi$  

• 0 and 0

• 1 and 1

• 1 and -1

• -1 and -1

The Fourier series is a combination of -----and ---- trigonometric terms

• sine and co secant

• tangent and cotangent

• sine and cosine

• cosine and secant

Identify Even function from the following

• x+x²

• x² + x³

• x²

• 1+x

Identify odd function

• 1+x+x²

• x+2

• x-x³

• x² + x⁴

The Fourier constant b_n for f(x)= x sinx in (-2,2) is

• 2

• 1

• 0

• 4

The trigonometric Fourier series of an even function does not have

• Sine terms

• Cosine terms

• Constant term

• harmonic terms

If f(x) = sinh(x) defined in -π<x<π then a₀ and a_n values are

• a₀ = 0 , a_n = 1

• a₀ = 1 , a_n = 1

• a₀ = 0 , a_n = 0

• a₀ = 1 , a_n = 1

Which of the following functions cannot be expressed as a Fourier series ?

• tanx

• x

• xsinx

• cosx

 $If\ b_n\ =\frac{4}{n\pi}\left\{1-\left(-1\right)^n\right\}\ ,\ What\ is\ the\ value\ of\ b_3\ ?$  

•  $\frac{4}{n\pi}$  

•  $\frac{8}{n\pi}$  

•  $\frac{-8}{n\pi}$  

• 0

The Fourier coefficient a₀ for f(x) = e^x in (0,2π) is

• e^2π-1/π

• e^2π-1/2π

• e^2π-1

• 0